An intermediate concept is that of a De Morgan algebra, which is an Ockham algebra with the additional requirement that ¬⁡(¬⁢a)=a.

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In the category of Ockham algebras, the morphism between any two objects is a {0,1}-lattice homomorphism (http://planetmath.org/LatticeHomomorphism) f that preserves ¬: f⁢(¬⁢a)=¬⁢f⁢(a). In fact, f⁢(0)=f⁢(¬⁢1)=¬⁢f⁢(1)=¬⁢1=0, so that it is safe to drop the assumption that f preserves 0.